45 citations · 96 across the 15 of their papers we have counts for
17 papers
Optimization for the first weighted eigenvalue of local-nonlocal operators with a potential
R. Lakshmi, Sekhar Ghosh, Ratan Kr. Giri
In this work, we study the optimization problem for the first eigenvalue of mixed local nonlocal operators plus a potential . We begin by investigating the existence and fundame…
On weak and viscosity solutions to a nonhomogeneous mixed local-nonlocal equation
R. Lakshmi, Sekhar Ghosh
This paper explores the relationship between weak and viscosity solutions to a nonhomogeneous mixed local and non-local -Laplace equation in a bounded Lipschitz domain in $\math…
On equivalence of weak and viscosity solutions to nonlocal double phase problems with nonhomogeneous data
Sekhar Ghosh, R. Lakshmi, Chao Zhang
This work focuses on the nonhomogeneous nonlocal double phase problem \begin{align*} L_au(x)=f(x,u,D_s^p u, D_{a,t}^q u) \text{ in } Ω, \end{align*} where is…
Brezis-Nirenberg type problems associated with nonlinear superposition operators of mixed fractional order
Yergen Aikyn, Sekhar Ghosh, Vishvesh Kumar +1
This paper aims to study the Brezis-Nirenberg type problem driven by the nonlinear superposition of operators of the form wher…
Critical Equations Involving Nonlocal Subelliptic Operators on Stratified Lie Groups: Spectrum, Bifurcation and Multiplicity
Sekhar Ghosh, Vishvesh Kumar
In this paper, we explore the bifurcation phenomena and establish the existence of multiple solutions for the nonlocal subelliptic Brezis-Nirenberg problem: \begin{equation*} \begi…
Existence results for mixed local and nonlocal elliptic equations involving singularity and nonregular data
Souvik Bhowmick, Sekhar Ghosh
In this paper, we prove the existence of weak, veryweak and duality solutions to a class of elliptic problems involving singularity and measure data which is given by: $-Δu+(-Δ)^s…
Subelliptic Nonlocal Brezis-Nirenberg Problems on Stratified Lie Groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
In this paper, we investigate the subelliptic nonlocal Brezis-Nirenberg problem on stratified Lie groups involving critical nonlinearities, namely, \begin{align*} (-Δ_{\mathbb{G},…
A weighted eigenvalue problem for mixed local and nonlocal operators with potential
R. Lakshmi, Ratan Kr. Giri, Sekhar Ghosh
We study an {\it indefinite weighted eigenvalue problem} for an operator of {\it mixed-type} (that includes both the classical {\it -Laplacian} and the {\it fractional -Lapla…
Best constants in subelliptic fractional Sobolev and Gagliardo-Nirenberg inequalities and ground states on stratified Lie groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
In this paper, we establish the sharp fractional subelliptic Sobolev inequalities and Gagliardo-Nirenberg inequalities on stratified Lie groups. The best constants are given in ter…
Compact Embeddings, Eigenvalue Problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups
Sekhar Ghosh, Vishvesh Kumar, Michael Ruzhansky
The purpose of this paper is twofold: first we study an eigenvalue problem for the fractional -sub-Laplacian over the fractional Folland-Stein-Sobolev spaces on stratified Lie g…
Existence of at least solutions to a fractional -Kirchhoff problem involving singularity and critical exponent
Sekhar Ghosh, Debajyoti Choudhuri, Alessio Fiscella
We study the existence of nonnegative solutions to the following nonlocal elliptic problem involving singularity \begin{align} \mathfrak{M}\left(\int_{Q}\frac{|u(x)-u(y)|^p}{|x-y|^…
Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity
Sekhar Ghosh, Debajyoti Choudhuri, Ratan Kr. Giri
We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-Δ)_{p(\cdot…
Least energy sign-changing solution of fractional -Laplacian problems involving singularities
Sekhar Ghosh, Kamel Saoudi, Mouna Kratou +1
In this paper we study the existence of a least energy sign-changing solution to a nonlocal elliptic PDE involving singularity by using the Nehari manifold method, the constraint v…
Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity
S. Ghosh, D. Choudhuri
In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE. \begin{align} (-Δ)^s u&= \fracλ{u^γ}+ f(x,u)~\text{i…
Multiplicity and Hölder regularity of solutions for a nonlocal elliptic PDE involving singularity
Kamel Saoudi, Sekhar Ghosh, Debajyoti Choudhuri
In this paper, we prove the existence of multiple solutions for a nonlinear nonlocal elliptic PDE involving a singularity which is given as \begin{eqnarray} (-Δ_p)^s u&=& \fracλ{u^…
Multiplicity of solutions to an elliptic problem with singularity and measure data
S. Ghosh, A. Panda, D. Choudhuri
In this paper, we prove the existence of multiple nontrivial solutions of the following equation. \begin{align*} \begin{split} -Δ_{p}u & = \fracλ{u^γ}+g(u)+μ~\mbox{in}\,\,Ω, u & =…
Elliptic Partial Differential Equation Involving a Singularity and a Radon measure
A. Panda, S. Ghosh, D. Choudhuri
The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure as its nonhomo…